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13-XX
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G
Commutative rings and algebras
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13-00
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General reference works (handbooks, dictionaries, bibliographies, etc.)
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13-01
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Instructional exposition (textbooks, tutorial papers, etc.)
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13-02
|
Research exposition (monographs, survey articles)
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|
13-03
|
Historical {!must also be assigned at least one classification number from section 01}
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13-04
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Explicit machine computation and programs (not the theory of computation or programming)
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13-06
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Proceedings, conferences, collections, etc.
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13Axx
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General commutative ring theory
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13A02
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Graded rings
[See also
16W50]
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|
13A05
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Divisibility
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|
13A10
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Radical theory
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|
13A15
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Ideals; multiplicative ideal theory
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13A18
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Valuations and their generalizations
[See also
12J20]
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13A30
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Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics
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13A35
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Characteristic $p$ methods (Frobenius endomorphism) and reduction to characteristic $p$; tight closure
[See also
13B22]
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13A50
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Actions of groups on commutative rings; invariant theory
[See also
14L25]
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13A99
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None of the above, but in this section
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13Bxx
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Ring extensions and related topics
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13B02
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Extension theory
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|
13B05
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Galois theory (commutative rings)
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13B10
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Morphisms
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13B21
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Integral dependence
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13B22
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Integral closure of rings and ideals; integrally closed rings, related rings (Japanese, etc.)
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13B24
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Going up; going down; going between
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13B25
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Polynomials over commutative rings
[See also
11C08,
13F20,
13M10]
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13B30
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Quotients and localization
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13B35
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Completion
[See also
13J10]
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13B40
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\'Etale and flat extensions; Henselization; Artin approximation
[See also
13J15,
14B12,
14B25]
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13B99
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None of the above, but in this section
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13Cxx
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Theory of modules and ideals
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|
13C05
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Structure, classification theorems
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13C10
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Projective and free modules and ideals
[See also
19A13]
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13C11
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Injective and flat modules and ideals
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13C12
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Torsion modules and ideals
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13C13
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Other special types
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13C14
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Cohen-Macaulay modules
[See also
13H10]
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13C15
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Dimension theory, depth, related rings (catenary, etc.)
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13C20
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Class groups
[See also
11R29]
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13C40
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Linkage, complete intersections and determinantal ideals
[See also
14M12]
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13C99
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None of the above, but in this section
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13Dxx
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Homological methods
{For noncommutative rings, see
16Exx;
for general categories, see
18Gxx}
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13D02
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Syzygies and resolutions
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13D03
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(Co)homology of commutative rings and algebras (e.g., Hochschild, Andr\'e-Quillen, cyclic, dihedral, etc.)
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13D05
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Homological dimension
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13D07
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Homological functors on modules (Tor, Ext, etc.)
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13D10
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Deformations and infinitesimal methods
[See also
14B10,
14B12,
14D15,
32Gxx]
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13D15
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Grothendieck groups, $K$-theory
[See also
14C35,
18F30,
19Axx,
19D50]
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13D22
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Homological conjectures (intersection theorems)
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13D25
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Complexes
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13D30
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Torsion theory
[See also
13C12,
18E40]
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13D40
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G
Hilbert-Samuel and Hilbert-Kunz functions; Poincar\'e series
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13D45
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Local cohomology
[See also
14B15]
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13D99
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None of the above, but in this section
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13Exx
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Chain conditions, finiteness conditions
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|
13E05
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Noetherian rings and modules
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13E10
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Artinian rings and modules, finite-dimensional algebras
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13E15
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Rings and modules of finite generation or presentation; number of generators
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13E99
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None of the above, but in this section
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13Fxx
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Arithmetic rings and other special rings
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|
13F05
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Dedekind, Pr\"ufer and Krull rings and their generalizations
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13F07
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Euclidean rings and generalizations
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13F10
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Principal ideal rings
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13F15
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Factorial rings, unique factorization domains
[See also
14M05]
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13F20
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Polynomial rings and ideals; rings of integer-valued polynomials
[See also
11C08,
13B25]
|
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13F25
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Formal power series rings
[See also
13J05]
|
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13F30
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Valuation rings
[See also
13A18]
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13F40
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Excellent rings
|
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13F45
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Seminormal rings
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13F50
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Rings with straightening laws, Hodge algebras
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13F55
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Face and Stanley-Reisner rings; simplicial complexes
[See also
55U10]
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13F99
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None of the above, but in this section
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13G05
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Integral domains
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13Hxx
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Local rings and semilocal rings
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13H05
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Regular local rings
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13H10
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Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
[See also
14M05]
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13H15
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Multiplicity theory and related topics
[See also
14C17]
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13H99
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None of the above, but in this section
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|
13Jxx
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Topological rings and modules
[See also
16W60,
16W80]
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13J05
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Power series rings
[See also
13F25]
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13J07
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Analytical algebras and rings
[See also
32B05]
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13J10
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Complete rings, completion
[See also
13B35]
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13J15
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Henselian rings
[See also
13B40]
|
|
13J20
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Global topological rings
|
|
13J25
|
Ordered rings
[See also
06F25]
|
|
13J30
|
Real algebra
[See also
12Dxx,
14Pxx]
|
|
13J99
|
None of the above, but in this section
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|
13K05
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Witt vectors and related rings
|
|
13L05
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Applications of logic to commutative algebra
[See also
03Cxx,
03Hxx]
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13Mxx
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Finite commutative rings
{For number-theoretic aspects, see
11Txx}
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13M05
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Structure
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|
13M10
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Polynomials
|
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13M99
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None of the above, but in this section
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13Nxx
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Differential algebra
[See also
12H05,
14F10]
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13N05
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Modules of differentials
[See also
16S32]
|
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13N10
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Rings of differential operators and their modules
[See also
16S32,
32C38]
|
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13N15
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Derivations
|
|
13N99
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None of the above, but in this section
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13Pxx
|
Computational aspects of commutative algebra
[See also
68W30]
|
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13P05
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Polynomials, factorization
[See also
12Y05]
|
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13P10
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Polynomial ideals, Gr\"obner bases
[See also
13F20]
|
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13P99
|
None of the above, but in this section
|